Learning linguistic generalizations from only a few examples is a challenging task. Recent work has shown that program synthesis – a method to learn rules from data in the form of programs in a domain-specific language – can be used to learn phonological rules in highly data-constrained settings. In this paper, we use the problem of phonological stress placement as a case to study how the design of the domain-specific language influences the generalization ability when using the same learning algorithm. We find that encoding the distinction between consonants and vowels results in much better performance, and providing syllable-level information further improves generalization. Program synthesis, thus, provides a way to investigate how access to explicit linguistic information influences what can be learnt from a small number of examples.